A dimensionless measure of how much an orbit deviates from a perfect circle, ranging from 0 (circular) to 1 (highly elongated).Orbital eccentricity is a dimensionless number that quantifies how much an orbit deviates from a perfect circle. It ranges from 0 (a perfectly circular orbit) to values approaching 1 (a highly elongated, almost parabolic path). In celestial mechanics, this parameter is fundamental for describing the shape of any orbit — from planets around stars to stars around supermassive black holes. The concept is central to understanding why some orbits are stable, why others precess, and how gravitational interactions between bodies can distort their paths over time.
The concept was formalized by Johannes Kepler in the early 17th century, who used it in his laws of planetary motion to describe the elliptical orbits of planets around the Sun.
The eccentricity is derived from the conic section that describes the orbit: circles have eccentricity 0, ellipses have values between 0 and 1, parabolas exactly 1, and hyperbolas greater than 1. For a bound orbit (elliptical), the eccentricity determines the ratio of the semi-minor to semi-major axis, and thus how 'squashed' the ellipse is. In a two-body problem, eccentricity is conserved, but in multi-body systems or in the presence of relativistic effects, it can change over time — leading to phenomena like orbital precession or eccentricity oscillations.
Orbital eccentricity is used in satellite mission design to plan transfer orbits, in astrophysics to study the dynamics of binary black holes and exoplanets, and in calculating gravitational wave signals from eccentric mergers.
Mercury has the highest orbital eccentricity of any planet in the Solar System (about 0.2056), which made it a key test case for Einstein's general relativity.
